A053845 -id:A053845 - cp's OEIS frontend

A120291 Numerator of determinant of n X n matrix with elements M[i,j] = (1+Prime[i])/Prime[i] if i=j and 1 otherwise.

3, 1, 11, 3, 29, 1, 59, 1, 101, 1, 1, 3, 239, 47, 1, 191, 21, 251, 569, 64, 1, 12, 25, 482, 1061, 1, 1, 98, 1481, 797, 1721, 926, 3, 8, 3, 1214, 1, 458, 1, 1544, 99, 1724, 1213, 1916, 1, 2, 1, 3, 4889, 853, 5351, 1, 49, 3041, 2113, 3301, 6871, 3571, 2473, 10, 2661

Offset: 1

Alexander Adamchuk, Jul 08 2006, Aug 19 2006

Many a(n), such as 3,11,29,59,101,239,569,1061,1481,1721,4889.., are primes of form p(1)+...+p(k)+1 where p(i) =i-th prime A053845. It appeares that all primes of this form are presented in a(n) in their natural order.

Indices n such that a(n) = 1 are {2,6,8,10,11,15,21,26,27,37,39,45,47,52,75,84,87,88,91,94,...} = A121744[n] Numbers n such that (1 + Sum[Prime[k],{k,1,n}]) = (1 + A007504[n]) divides primorial number p(n)# = Product[Prime[k],{k,1,n}] = A002110[n].

Cf. A024528, A053845.

Cf. A121744, A007504, A002110.

Numerator[Table[Det[DiagonalMatrix[Table[1/Prime[i],{i,1,n}]]+1],{n,1,70}]]
Table[Numerator[(1+Sum[Prime[k],{k,1,n}])/Product[Prime[k],{k,1,n}]],{n,1,100}]

a(n) = numerator[Det[DiagonalMatrix[Table[1/Prime[i],{i,1,n}]]+1]].

a(n) = Numerator[ (1 + Sum[ Prime[k], {k,1,n} ]) / Product[ Prime[k], {k,1,n} ] ]. a(n) = Numerator[ (1 + A007504[n]) / A002110[n] ].

A257077 a(n) = prime(n)-prime(1)-prime(2)-...-prime(k), while the result > 0.

Original entry on oeis.org

2, 1, 3, 2, 1, 3, 7, 2, 6, 1, 3, 9, 13, 2, 6, 12, 1, 3, 9, 13, 15, 2, 6, 12, 20, 1, 3, 7, 9, 13, 27, 2, 8, 10, 20, 22, 28, 3, 7, 13, 19, 21, 31, 33, 37, 2, 14, 26, 30, 32, 36, 1, 3, 13, 19, 25, 31, 33, 39, 43, 2, 12, 26, 30, 32, 36, 3, 9, 19, 21, 25, 31, 39

Offset: 1

Carlos Eduardo Olivieri, Apr 15 2015

It appears that a(n) = n occurs only for n=3, 7, 13. It also appears that a(n+1) is never equal to a(n).
The list of indices such that a(n)=1 correspond to the primes in A053845. - Michel Marcus, Apr 16 2015
In other words, a(n) = prime(n) - A007504(k) for largest k such that prime(n) > A007504(k). - Danny Rorabaugh, Apr 20 2015

			a(1) = 2, since there is no previous prime.
a(2) = 1, since 3 - 2 = 1.
a(3) = 3, since 5 - 2 = 3.
a(4) = 2, since 7 - 2 - 3 = 2.
a(5) = 1, since 11 - 2 - 3 - 5 = 1.
a(6) = 3, since 13 - 2 - 3 - 5 = 3.
a(13) = 13, since 41 - 2 - 3 - 5 - 7 - 11 = 13.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A007504, A013918.

lst = {}; i = 1; While[i <= 1000, x = Prime[i]; k = 1; While[x > 0, x -= Prime[k]; k++]; x += Prime[k - 1]; AppendTo[lst, x]; i++]; lst

a(n) = {s = prime(n); k = 1; while ((ns = (s - prime(k))) > 0, s = ns; k++); s;} \\ Michel Marcus, Apr 16 2015

s=0; q=2; forprime(p=2,10, if(s+q>p, s+=q; q=nextprime(q+1)); print1(p-s", ")) \\ Charles R Greathouse IV, Apr 22 2015

a(n) << sqrt(n)*log(n). - Charles R Greathouse IV, Apr 23 2015

cp's OEIS Frontend

A120291 Numerator of determinant of n X n matrix with elements M[i,j] = (1+Prime[i])/Prime[i] if i=j and 1 otherwise.

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